Finite Group Databasebeta

← #16829736

Subgroups — #16829736

Order 3712.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271768C211yesmaximal, characteristic, complemented
2#14271637C211yesmaximal, characteristic, complemented
3#14271488C212yesmaximal, complemented
4#14271464C212yesmaximal, complemented
5#14271359C212yesmaximal, complemented
6#14271299C212yesmaximal, complemented
7#14271276C212yesmaximal, complemented
8C4×D232C212yesmaximal, complemented
9C29×#433C211yesmaximal, characteristic, complemented
10C22×D116C2211yescharacteristic
11C29×#117C2211yescharacteristic
12#11745292C2212yes—
13#11745288C2211yescharacteristic
14C2×D232C2212yes—
15C2×D232C2212yes—
16#11745256—22no—
17#11745255—22no—
18#11745246—22no—
19C22⋊C4×D29—22no—
20#11745236C2211yescharacteristic, complemented
21C4×D116C2212yes—
22C4×D116C2212yes—
23C4×D116C2212yescomplemented
24#11745232C2211yescharacteristic, complemented
25C29×C4⋊C8C2212yescomplemented
26C29×C22⋊C8C2212yes—
27C29×#97C2211yescharacteristic, complemented
28C4×C8×C29C2211yescharacteristic, complemented
29#11745169C2212yes—
30#11745169C2212yes—
31#11745169C2212yescomplemented
32#11745169C2212yescomplemented
33#11745166C2212yescomplemented
34#11745165C2212yescomplemented
35C23×D29—21no—
36C22×C4×C29C2311yescharacteristic
37C2×C22⋊D29—22no—
38C2×D116—21no—
39C2×D116—24no—
40C2×D116—22no—
41C2×D116C2312yes—
42C2×D116C2312yes—
43C2×C4×D29—22no—
44C2×C4×D29—22no—
45C2×C4×D29—22no—
46C2×C8×C29C2312yes—
47C2×C8×C29C2312yes—
48C4⋊C4×C29D412yes—
49C22⋊C4×C29D412yes—
50C42×C29C2311yescharacteristic
51C42×C29C2311yescharacteristic
52C22⋊Dic29—21no—
53#90781—22no—
54#90781—22no—
55#90781—22no—
56#90781—22no—
57C4⋊Dic29C2312yes—
58C4⋊Dic29C2312yes—
59#90779—22no—
60C4×Dic29—21no—
61D232—24no—
62D232—24no—
63C23×C29C2×D411yescharacteristic
64C22×D29—22no—
65C22×D29—24no—
66C22×D29—22no—
67C22×D29—82no—
68C2×C4×C29—22no—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D412yes—
71C2×C4×C29C2×D412yes—
72C2×C4×C29C2411yescharacteristic
73C22⋊D29—82no—
74C2×Dic29—22no—
75C2×Dic29—22no—
76D116—24no—
77D116—22no—
78D116—22no—
79D116—22no—
80D116—82no—
81D116#4114yes—
82C4×D29—82no—
83C4×D29—82no—
84C4×D29—82no—
85C8×C29—22no—
86C8×C29—22no—
87#3122—291nomaximal, Sylow
88C22×C29—21no—
89C22×C29—22no—
90C22×C29C22×D411yescharacteristic
91C2×D29—24no—
92C2×D29—42no—
93C2×D29—42no—
94C2×D29—42no—
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—84no—
98C4×C29—21no—
99C4×C29—22no—
100C4×C29—22no—
101C4×C29C2×#4112yes—
102Dic29—42no—
103Dic29—42no—
104#540—291no—
105#518—291no—
106#482—292no—
107#478—292no—
108#459—292no—
109#447—292no—
110#442—292no—
111C4×D8—292no—
112#433D2911yescharacteristic, complemented
113C2×C29—41no—
114C2×C29#52511yescharacteristic
115C2×C29#57612yes—
116D29—44no—
117D29—82no—
118C22×D4—291no—
119C2×D8—292no—
120C2×D8—292no—
121#127—291no—
122#125—291no—
123#123—582no—
124#121—292no—
125#121—582no—
126C4×D4—292no—
127C4×D4—292no—
128C4×D4—292no—
129C4×D4—582no—
130#117—291no—
131#117C2×D2911yescharacteristic
132C2×C22⋊C4—582no—
133#107—292no—
134#106—292no—
135C4⋊C8C2×D2912yescomplemented
136#102—292no—
137#102—292no—
138#102—292no—
139#102—292no—
140C22⋊C8C2×D2912yes—
141#97C2×D2911yescharacteristic, complemented
142C4×C8C2×D2911yescharacteristic, complemented
143C29#312211yescharacteristic, complemented, Sylow
144C24—581no—
145C2×D4—292no—
146C2×D4—292no—
147C2×D4—584no—
148C2×D4—582no—
149C2×D4—581no—
150C2×D4—582no—
151C22×C4—582no—
152C22×C4—582no—
153C22×C4—582no—
154C22×C4C22×D2911yescharacteristic
155D8—584no—
156D8—584no—
157C2×C8C22×D2912yes—
158C2×C8C22×D2912yes—
159C4⋊C4—292no—
160C4⋊C4—292no—
161C4⋊C4—582no—
162C4⋊C4D11612yes—
163C22⋊C4—581no—
164C22⋊C4—582no—
165C22⋊C4—582no—
166C22⋊C4—582no—
167C22⋊C4—582no—
168C22⋊C4D11612yes—
169C42—581no—
170C42C22×D2911yescharacteristic
171C42C22×D2911yescharacteristic
172C23—584no—
173C23—582no—
174C23—582no—
175C23—2322no—
176C23C2×D11611yescharacteristic
177D4—294no—
178D4—584no—
179D4—582no—
180D4—582no—
181D4—582no—
182D4—2322no—
183D4—2322no—
184C2×C4—22no—
185C2×C4—582no—
186C2×C4—582no—
187C2×C4—2322no—
188C2×C4—2322no—
189C2×C4—2322no—
190C2×C4C2×D11611yescharacteristic
191C2×C4C2×D11612yes—
192C2×C4C2×D11612yes—
193C2×C4C23×D2911yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—584no—
199C22—1162no—
200C22—1162no—
201C22—1162no—
202C22—1162no—
203C22—1162no—
204C22—2324no—
205C22C22×D11611yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—1162no—
210C4—1162no—
211C4#41×D2912yes—
212C2—41no—
213C2—1164no—
214C2—2322no—
215C2#1427167511yescharacteristic
216C2#1427196812yes—
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#433C2
socleC22×C29C22×D4
hypercenter#433D29
hypocenterC29#3122
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14271768C2semidirect
2. #14271637C2semidirect
3. #14271488C2semidirect
4. #14271464C2semidirect
5. #14271359C2semidirect
6. #14271299C2semidirect
7. #14271276C2semidirect
8. C4×D232C2semidirect
9. C29×#433C2semidirect
20. #11745236C22semidirect
23. C4×D116C22semidirect
24. #11745232C22semidirect
25. C29×C4⋊C8C22semidirect
27. C29×#97C22semidirect
28. C4×C8×C29C22semidirect
31. #11745169C22semidirect
32. #11745169C22semidirect
33. #11745166C22semidirect
34. #11745165C22semidirect
112. #433D29semidirect
135. C4⋊C8C2×D29semidirect
141. #97C2×D29semidirect
142. C4×C8C2×D29semidirect
143. C29#3122semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#142717682
#142716372
#142714882
#142714642
#142713592
#142712992
#142712762
C4×D2322
C29×#4332
#312229